It is common practice to inspect work pieces subsequent to production on a coordinate positioning apparatus, such as a coordinate measuring machine (CMM), in order to check for correctness of predefined object parameters, like dimensions and shape of the object.
In a conventional 3-D coordinate measurement machine, a probe head is supported for movement along three mutually perpendicular axes (in directions X, Y and Z). Thereby, the probe head can be guided to any arbitrary point in space of a measuring volume of the coordinate measuring machine and the object is measurable with a measurement sensor (probe) carried by the probe head.
In a simple form of the machine a suitable transducer mounted parallel to each axis is able to determine the position of the probe head relative to a base of the machine and, therefore, to determine the coordinates of a measurement point on the object being approached by the sensor. For providing movability of the probe head a typical coordinate measuring machine may comprise a frame structure on which the probe head is arranged and driving means for moving frame components of the frame structure relative to each other.
For measuring surface variations, both measurement principles based on use of tactile sensors and of optical sensors are known.
In general, to provide a coordinate measuring machine with an improved measurement precision, its frame structure is therefore usually designed to have a high static stiffness. In order to achieve a stiff and rigid machine design, the frame structure or at least parts of it, is often made of stone, such as granite. Besides all the positive effects like thermal stability and good damping properties, the granite also makes the machine and the movable frame elements quite heavy. The high weight on the other side also requires high forces for a decent acceleration.
There are still several possible sources of error, if such technique is employed. Resonances or vibrations of machine parts when moving one frame component relative to another component are just two examples for dynamic errors. Additionally, static errors like lack of straightness in movement and of orthogonality of the axes or lateral offset in the linear drive mechanisms may occur.
According to many approaches the mentioned errors are only analyzed statically, although they also comprise dynamic factors which are dependent on the movement of the axes, in particular dependent on the position, speed, acceleration and jerk when moving the axis. With the speed-dependent calibration, this fact is taken into account in a rather simple and inflexible way. While the static errors can be numerically reduced by the use of position calibration matrices, things get much more complex when trying to compensate the dynamic errors.
The calibration gets even more complex when taking into account the dynamic errors, such as mentioned vibrations or resonance or dynamic forces etc. which errors can not only influence the axis on which they are occurring, but which can also “crosstalk” to other axes and cause errors in other parts of the system. Furthermore, the underlying effects can also be dependent on environmental conditions such as temperature, humidity, air-pressure, etc. and in particular, they will also vary over the lifetime of the machine.
In that context, for example, it has to be considered that accelerations of one axis of the machine (which can move further perpendicular axes and the probe head), can cause linear and angular dynamic deflections of the whole frame of the coordinate measuring machine, which in turn cause measurement uncertainties and errors. These dynamic measurement errors may be reduced by taking measurements at low accelerations, e.g. by a consequently optimized trajectory of desired movement.
Known approaches are trying to suppress deflections, vibrations and/or oscillations caused by the acceleration of the machine by a technology called input-shaping, which controls the regulating variable, e.g. the force or current of a propulsion motor, in such a way as to bypass mechanical resonances and avoid a stimulation of resonance frequencies or even actively counterforce oscillations by a accordingly manipulated variable on the output to the driving actuator control.
Also model predictive control, as a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open-loop optimal control problem, using the current state of the plant as the initial state, can be applied to CMMs. The optimisation yields an optimal control sequence and the first control in the sequence is then applied to the plant.
Exemplarily for error handling, EP 1 559 990 discloses a coordinate measuring system and method of correcting coordinates measured in a coordinate measuring machine, measuring geometrical errors while parts with various weights are mounted on the coordinate measuring machine. Compensation parameters are derived from measured results per a weight of a part and stored. A compensation parameter corresponding to a weight of a part to be measured is appropriately read out to correct measured coordinates of the part to be measured.
As a further example, EP 1 687 589 discloses a method of error compensation in a coordinate measuring machine with an articulating probe head having a surface detecting device. The surface detecting device is rotated about at least one axis of the articulating probe head during measurement. The method comprises the steps of: determining the stiffness of the whole or part of the apparatus, determining one or more factors which relate to the load applied by the articulating probe head at any particular instant and determining the measurement error at the surface sensing device caused by the load.
Another approach for error correction of work piece measurements with a coordinate measuring machine (CMM) is disclosed in GB 2 425 840. Thereby, position measurements are taken with a work piece sensing probe, in which means of measuring acceleration are provided. The measurements are corrected for both high frequency (unrepeatable) errors such as those due to vibration, and low frequency (repeatable) errors such as those due to centrifugal forces on the probe. The correction method comprises measuring the work piece, determining repeatable measurement errors from a predetermined error function, error map or error look-up table, measuring acceleration and calculating unrepeatable measurement errors, combining the first and second measurement errors to determine total errors and correcting the work piece measurements using the total errors. The predetermined error map is calculated using an artefact of known dimensions.
It is also known to use accelerometers fitted in the probe or on other moving parts of the measurement machine, e.g. the Z-column and/or in the base table, allowing a differential measurement and/or the evaluation of externally applied vibrations. In such an arrangement, the displacements and errors of the probe-position can be measured with double integration and, based on this information, it is possible to adjust the reading with the difference between the doubly integrated signal and the scales. For instance, such a quasi-static approach is disclosed by WO 02/04883.
For handling above mentioned errors, in particular dynamic errors, usually a suitable model of the CMM is to be defined, wherein a positioning behaviour of especially the frame structure of the CMM is enabled to be described based on that model. Exemplarily, a look-up table may be defined in order to lookup a correction value correlated with an actual positioning of the frame components of the CMM. Such modelling of a CMM becomes more important along with weight (and stiffness) reduction of CMM-parts.
Weight reduction is a main topic relating to the designs of coordinate measuring machines, as if the machine components are built comprising less weight (and less stiffness) faster positioning of respective components can be achieved by causing fewer force affecting the coordinate measuring machine. On the other hand the influence of machine vibrations and torsions caused by reduced stiffness and (faster) movement of the machine components increase with weight reduction of these parts. Thus, uncertainties of derived measurement values and errors occurring from such deformations and vibrations increase accordingly. Known modelling for providing error compensation of coordinate measuring machines does not enable to calculate and compensate for the increased amount of errors influencing the measuring performance of a CMM. Moreover, such modelling does not enable to handle or to determine different kinds of errors continuously with high precision in order to compensate measuring values derived with weight reduced CMMs.
Since models are only an approximation of reality, they are prone to errors due to parameter inaccuracy and modelling simplifications. Especially, when the model system includes one or more natural modes with low damping, these errors can become significant. The model-reality mismatch may be caused by a simplified model, by inaccurate model parameters, such as masses, inertias, stiffness values, damping values or geometrical properties, or by time- and/or position-varying parameters, such as air-bearing stiffness and damping.
Whereas masses, inertias, geometrical properties and stiffness values can accurately be determined from e.g. CAD models, the retrieval of damping values or bearing characteristics is more challenging. Parameters especially prone to mismatch are the air bearing stiffness and damping values, since they vary in a nonlinear behaviour with air bearing pressure change, orientation changes, surface characteristics and the movement speed.
Often the input variables of the model (e.g. acceleration) exhibit large measurement noise, sometimes due to cross-coupling into the sensing axis (e.g. from an acceleration sensor). These input variables (sensor data) may be low-pass filtered, which introduces frequency dependent phase shifts (and frequency dependent delays) and, thus, this introduces errors in the calculation of the deflection.